29:T4b4,# Introduction Trillions upon trillions of messages zip between Earth and neighboring galaxies every millisecond. But transmitting over such long distances is tricky. Pesky solar flares, temporal distortions, stray forces, and even the flap of a space butterfly's wing can cause a random bit to change during transmission. Now imagine the consequences: - Crashing the Intergalactic Share Market when "buy low" turns to "sell now". - Losing contact with the Kepler Whirl system when "save new worm hole" becomes "cave new worm hole". - Or plunging the universe into existential horror by replacing a cowboy emoji 🤠 with a clown emoji 🤡. Detecting corrupted messages isn't just important — it's critical. The receiver _must_ know when something has gone wrong before disaster strikes. But how? Scientists and engineers from across the universe have been battling this problem for eons. Entire cosmic AI superclusters churn through the data. And then, one day, a legend resurfaces — an ancient, powerful method, whispered in debugging forums, muttered by engineers who've seen too much... The Parity Bit! A method so simple, so powerful, that it might just save interstellar communication. 2a:T490,def parity (data: i32): i32 = let (bit, _) = loop (bit, byte) = (0, data) while byte != 0 do (1 - bit, byte ^ (byte & -byte)) in bit def encode (data: i32): i32 = ((data & 0x7f) << 1) | parity (data & 0x7f) def transmit_sequence [n] (message: [n]i32): []i32 = let (a, i, data, count) = loop (a, i, data, count) = (replicate ((n * 8 + 6) / 7) 0, 0, 0, 0) for byte in message do let data2 = (data << 8) | byte let count2 = count + 1 let a2 = a with [i] = encode (data2 >> count2) let i2 = i + 1 in if count2 < 7 then (a2, i2, data2, count2) else (a2 with [i2] = encode (data2 >> (count2 - 7)), i2 + 1, data2, count2 - 7) in if count == 0 then a[0:i] else (a with [i] = encode (data << (7 - count)))[0:i + 1] def decode_message [n] (message: [n]i32): []i32 = let (a, _, _, _) = loop (a, i, data, count) = (replicate (n * 7 / 8) 0, 0, 0, 0) for byte in message do let data2 = assert (parity byte == 0) ((data << 7) | (byte >> 1)) let count2 = count + 7 in if count2 < 8 then (a, i, data2, count2) else (a with [i] = (data2 >> (count2 - 8)) & 0xff, i + 1, data2, count2 - 8) in a 2b:T10be,